2. Four Elastic Moduli
• There are four elastic moduli for a
unidirectional lamina
– Longitudinal Young’s Modulus E1
– Transverse Young’s Modulus E2
– Major Poisson’s ration v12
– In Plane Shear Modulus G12
3. Strength of Material Approach
Assumptions are made in the strength of materials
approach
• The bond between fibres and matrix is perfect.
• The elastic moduli, diameters, and space
between fibres are uniform.
• The fibres are continuous and parallel.
• The fibre and matrix follow Hooke’s law (linearly
elastic).
• The fibres possess uniform strength.
• The composites is free of voids.
4. Effective Tensors of Composites
• Quantum Mechanics and computation
• Homogenized quantum mechanical equations
5. Intuitive Homogenization
• Microscale with length less than l1
• The mesoscale, intermediate scale,
composites are statistically homogenous. Slow
variation at macroscopic level
• Macroscale is greater than l3, and less than
relevant dimensions, and less than scale of
variation in macroscopic structure
9. Composites Design
Laminate Design
• Take advantage of the orthotropic nature of the
fibre composite ply.
– To carry in-plane tensile or compressive loads align the
fibres in the directions of these loads.
– For in-plane shear loads, align most fibers at ± 45° to
these shear loads.
– For combined normal and shear in-plane loading
provide multiple or intermediate ply angles for a
combined load capability.
10. Composites Design
Laminate Design
• Intersperse the ply orientations.
– If a design requires a laminate with 16 plies at ±45°, 16 plies at 0°, and 16 plies
at 90°, use the interspersed design (902/ ±452/02)4s rather than (908/ ±458/08)s.
– Concentrating plies at nearly the same angle (0° and 90° in this
example)provides the opportunity for large matrix cracks to form. These
produce lower laminate allowables, probably because large cracks are more
injurious to the fibres, and more readily form delaminations than the finer
cracks occurring in interspersed laminates.
– If a design requires all 0° plies, some 90° plies (and perhaps some off-angle
plies ) should be interspersed in the laminate to provide some biaxial strength
and stability and to accommodate unplanned loads. This improves handling
characteristics, and serves to prevent large matrix cracks from forming.
– Locally reinforce with fabric or mat in areas of concentrated loading. (This
technique is used to locally reinforce pressure vessel domes)
– Ensure that the laminate has sufficient fibre orientations to avoid dependence
on the matrix for stability.
11. Composites Design
Laminate Design
• Select the lay-up to avoid mismatch of properties of the
laminate with those of the adjoining structures
– Poisson's ratio: if the transverse strain of a laminate greatly
differs from that of adjoining structure, large interlaminar
stresses are produced under load.
– Coefficient of thermal expansion: temperature change can
produce large interlaminar stresses if coefficient of thermal
expansion of the laminate differs greatly from that of adjoining
structure.
– The ply layer adjacent to most bonded joints should not be
perpendicular to the direction of loading. Thicken the composite
in the joint area, soften the composite by adding fiberglass or
angle plies and select the highest strain-capability adhesive.
12. Composites Design
Laminate Design
• Use multiple ply angles.
– Typical composite laminates are constructed from multiple
unidirectional or fabric layers which are positioned at angular
orientations in a specified stacking sequence. From many
choices, experience suggests a rather narrow range of practical
construction from which the final laminate configuration is
usually selected. The multiple layers are usually oriented in at
least two different angles, and possibly three or four;
(±0°,0°/±0° or 0 ° /±0° / 90 ° over most applications, with 0
between 30 and 60 degrees).
– Unidirectional laminates are rarely used except when the basic
composite material is only mildly orthotropic (e.g. certain métal
matrix applications) or when the load path is absolutely known
or carefully oriented parallel to the reinforcement
14. Composite Materials
• High strength reinforcements and high
performance matrix
• Increase vol fractions means increase in
composite properties
• Matrix: for compressive loads, shear capabilities,
transfer load internally, and in 2D provide
resistance to impact damage and delamination.
• Matrix is weaker than fibres with some
exceptions
15. Composite Materials
• Fibres are stronger than bulk form due to
• Smaller fibre dia and opportunity to align fibre
in preferred directions
• Early warnings due to large number of fibres
• High specific properties and reduction in layup
16. Glass Fibre
• Enabling technology
• Building, auto, rail, seagoing, racing crafts, commercial and
military aerospace applications
• Decorative panels, appliances, ship and boat hulls, light
aircraft and gliders, recreational eqpt, high pressure gas
containers and rocket motors
• Cost, availability, handling and process ability and useful
properties
• E-glass with very good mechanical and electrical
characteristics
• S- Glass with higher %age of alumina and higher specific
properties
• Silica fibres produced from E-glass for rocket motors
17. Carbon Fibre
• High performance resin based composites
• Military aerospace applications
• Thermal decomposition of organic precursors
• Rayan or PAN or pitch
• High elongation fibres with <2%
• New high modulus high strength fibres with
smaller dia
• Improvements in resins
18. Organic Fibres
• Aramid by DuPont
• Limited applications due to low fibre
compression
• High tensile strength and low density fibres to
replace S-glass
• High damage tolerance and cut resistance
• Low adhesion, moisture absorption, low
compression properties and diffiulties in
machining
